Answer: Option C
:
C
Number of moles present initially is $n=\frac{PV}{RT}$. Let $n^{\prime }$ be the number of moles of the gas that leaked till
the pressure falls to $P^{\prime }$. Since volume V of the vessel cannot change and temperature T remains
constant during leakage, we have
$n^{\prime }=\frac{P^{\prime }V}{RT}$
$\therefore$Number of moles that leaked is
$\Delta n=n-n^{\prime }=\frac{PV}{RT}-\frac{P^{\prime }V}{RT}=\frac{V}{RT}(P-P^{\prime })$
So the correct choice is (C)